An algebraic structure for the convolution of life distributions.

Abstract

In this paper one method for analytically describing the life distribution of a system is investigated. This is done by using the inherent properties of convolutions and mixtures of life distributions to create an algebraic structure. Once the algebraic structure is constructed it can be used to develop algorithms to go from the schematic of a system to its survival function. It is noted along the way that many combinations of constant failure rate components, e.g., redundant, series, or parallel systems can be described by a mixture of convolutions and that often these expressions can be greatly simplified.